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  • Evaluate the following limits limit z tends to 1 z^ 1 / 3 - 1

10.   Evaluate the following limits \lim_{z\rightarrow 1} \frac{z^{1/3}-1}{z^{1/6}-1}

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best_answer

The limit

\lim_{z\rightarrow 1} \frac{z^{1/3}-1}{z^{1/6}-1}

Here on directly putting limit , both numerator and the denominator becomes zero so we factorize the function and then put the limit.

\lim_{z\rightarrow 1} \frac{z^{1/3}-1}{z^{1/6}-1}=\lim_{z\rightarrow 1} \frac{z^{(1/6)^2}-1^2}{z^{1/6}-1}

=\lim_{z\rightarrow 1} \frac{(z^{(1/6)}-1)(z^{(1/6)}+1)}{z^{1/6}-1}

=\lim_{z\rightarrow 1} (z^{(1/6)}+1)}

= (1)(1/6) + 1

=1+1

=2  (Answer)

 

Posted by

Pankaj Sanodiya

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